pku2400 Supervisor, Supervisee 二分图最优匹配的全部解

pku2400 Supervisor, Supervisee 二分图最优匹配的全部解

题意：
给出职工对经理的评分和经理对职工的评分。求出所有的匹配方案，使得平均满意度最高

解法:
KM匹配出最优解后，根据标号遍历得所有解。注意，调整顶标以后合法匹配边仍然是l[i]+r[j]=val[i][j]

代码：

Source Code

Problem: 2400		User: yzhw
Memory: 408K		Time: 0MS
Language: G++		Result: Accepted

• Source Code

# include <cstdio>
# include <cstring>
# include <cstdlib>
using namespace std;
# define max(a,b) ((a)>(b)?(a):(b))
# define min(a,b) ((a)<(b)?(a):(b))
# define N 15
int map[N][N],match[N],ln[N],rn[N],n,c;
bool l[N],r[N];
bool dfs(int pos)
{
	//if(l[pos]) return false;
	l[pos]=true;
	for(int i=0;i<n;i++)
		if(!r[i]&&ln[pos]+rn[i]==map[pos][i])
		{
			r[i]=true;
			if(match[i]==-1||dfs(match[i]))
			{
				match[i]=pos;
				return true;
			}

		}
		return false;
}
void adjust()
{
	int minnum=0xfffffff;
	for(int i=0;i<n;i++)
		if(l[i])
			for(int j=0;j<n;j++)
				if(!r[j])
					minnum=min(minnum,ln[i]+rn[j]-map[i][j]);
	for(int i=0;i<n;i++)
	{
		if(l[i]) ln[i]-=minnum;
		if(r[i]) rn[i]+=minnum;
	}
}
void search(int now)
{
	if(now==n)
	{
		int ret[N];
		for(int i=0;i<n;i++)
			ret[match[i]]=i;
		printf("Best Pairing %d\n",++c);
		for(int i=0;i<n;i++)
			printf("Supervisor %d with Employee %d\n",i+1,ret[i]+1);
		//system("pause");
	}
	for(int i=0;i<n;i++)
		if(match[i]==-1&&ln[now]+rn[i]==map[now][i])
		{
			match[i]=now;
			search(now+1);
			match[i]=-1;
		}
}
int main()
{
	int test;
	scanf("%d",&test);
	for(int tt=1;tt<=test;tt++)
	{
		scanf("%d",&n);
		memset(map,0,sizeof(map));
		for(int i=0;i<n;i++)
			for(int j=0;j<n;j++)
			{
				int t;
				scanf("%d",&t);
				map[t-1][i]-=j;
			}
		for(int i=0;i<n;i++)
			for(int j=0;j<n;j++)
			{
				int t;
				scanf("%d",&t);
				map[i][t-1]-=j;
			}
		
		memset(match,-1,sizeof(match));
		memset(rn,0,sizeof(rn));
		for(int i=0;i<n;i++)
		{
			int maxnum=-0xfffffff;
			for(int j=0;j<n;j++)
				maxnum=max(maxnum,map[i][j]);
			ln[i]=maxnum;
		}
		double ans=0;
		for(int i=0;i<n;i++)
		{
			memset(l,false,sizeof(l));
			memset(r,false,sizeof(r));
			while(!dfs(i))
			{
				adjust();
				memset(l,false,sizeof(l));
				memset(r,false,sizeof(r));
			}
		}
		for(int i=0;i<n;i++)
			ans-=map[match[i]][i];
		printf("Data Set %d, Best average difference: %.6f\n",tt,ans/n/2.0);
		memset(match,-1,sizeof(match));
		c=0;
		search(0);
		printf("\n");
	}
	return 0;
}